Euclid and His Modern RivalsCourier Corporation, 1. jan. 2004 - 275 sider From the Oxford don who created 'Alice in Wonderland' comes a fanciful play that takes a hard look at late-nineteenth-century interpretations of Euclidean geometry. 'Euclid and His Modern Rivals' takes place in Hell, where the Infernal Judges are examining and passing judgment on contemporary theories of geometry. Books that reject Euclid's treatment of parallels receive first consideration (infinite series, angles made by transversals, equidistances, revolving lines, 'directions,' infinitesimals), followed by books that adopt Euclid's treatment, and ultimately, Euclid's own works. |
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Side v
... geometry more rigorous , or more palatable , by re- vising the definitions and rearranging the propositions . One by one , these rivals are ridiculed and put to shame . Time has justified Dodgson's scorn , for all save Legendre and ...
... geometry more rigorous , or more palatable , by re- vising the definitions and rearranging the propositions . One by one , these rivals are ridiculed and put to shame . Time has justified Dodgson's scorn , for all save Legendre and ...
Side vi
... geometry easier by introducing redundant " post- ulates " or " assumptions . " On page 57 we read , " . . . it is a generally admitted principle that , at least in dealing with beginners , we ought not to take as axiomatic any Theorem ...
... geometry easier by introducing redundant " post- ulates " or " assumptions . " On page 57 we read , " . . . it is a generally admitted principle that , at least in dealing with beginners , we ought not to take as axiomatic any Theorem ...
Side vii
... geometry . In these days of enlighten- ment we find it difficult to realize that , 100 years ago , Professors Arthur Cayley of Cambridge and W. K. Clif- ford of London may well have been the only Englishmen who understood the ...
... geometry . In these days of enlighten- ment we find it difficult to realize that , 100 years ago , Professors Arthur Cayley of Cambridge and W. K. Clif- ford of London may well have been the only Englishmen who understood the ...
Side viii
... Geometry , which I have been teaching for nearly five- and - twenty years , that I feel sufficiently familiar with the matter in hand to venture to speak . Let me take this opportunity of expressing my grati- tude , first to Mr ...
... Geometry , which I have been teaching for nearly five- and - twenty years , that I feel sufficiently familiar with the matter in hand to venture to speak . Let me take this opportunity of expressing my grati- tude , first to Mr ...
Side ix
... Geometry , to employ one text- book only ; secondly , that there are strong a priori reasons for retaining , in all its main features , and specially in its sequence and numbering of Propositions and in its treat- ment of Parallels ...
... Geometry , to employ one text- book only ; secondly , that there are strong a priori reasons for retaining , in all its main features , and specially in its sequence and numbering of Propositions and in its treat- ment of Parallels ...
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adjacent angles alternate angles angles are equal assert assume axiomatic beginners Cambridge Mathematical Tripos Certainly coincide coincidental Lines common point Contranominal Cor Cor course curve CUTHBERTSON deduce define Definition demonstration different directions different Lines drawn edition Elementary Geometry equal angles equally inclined equidistant equidistantial Euclid examining Felix Klein figure finite Lines given Line given point grant H. S. M. COXETER HENRICI interior angles interpolated intersectional Lines Legendre magnitude Manual mathematical mean meet if produced method Modern Rivals NIEMAND reads old proof Pair of Lines parallel perpendicular Petitio Principii phrase Plane Playfair's Axiom position Pr Pr Problems Prop Propositions prove right angles right Line separate point separational Lines sepcodal side straight angle straight Line suppose Syllabus teaching text-book Th Th Theorem tion transversal treatise Triangle true Unabridged republication undisputed Axioms Wilson words writer دو وو